1. Field of the Invention
The present invention relates to quantum dots. More particularly, the present invention relates to a method for forming at least one quantum dot at a predetermined location on a substrate, to a design for a lithographic mask for use with this method according to embodiments of the invention and to a method for making such a design as well as to semiconductor devices made with the at least one quantum dot.
2. Description of the Related Technology
Quantum dots are semiconductor nanostructures that confine the motion of conduction band electrons, valence band holes, or excitons (bound pairs of conduction band electrons and valence band holes) in all three spatial directions. Confinement can be due to electrostatic potentials (generated by external electrodes, doping, strain, impurities), the presence of an interface between different semiconductor materials (e.g. in core-shell nano-crystal systems), the presence of the semiconductor surface (e.g. semiconductor nano-crystal), or a combination of these.
Quantum dots have a discrete quantized energy spectrum. The corresponding wave functions are spatially localized within the quantum dot, but extend over many periods of the crystal lattice. Quantum dots contain a small finite number in the order of about 1-100 of elementary electric charges, i.e. a finite number of conduction band electrons, valence band holes, or excitons. The usefulness of quantum dots comes from their peak emission frequency's extreme sensitivity to both the dot's size and composition. This remarkable sensitivity is quantum mechanical in nature. Quantum dots offer the unnatural ability to tune the bandgap and hence the emission wavelength.
Electrons in quantum dots have a range of energies. The concepts of energy levels, bandgap, conduction band and valence band which apply to bulk semiconductors also apply to quantum dots. However, there is a major difference. Excitons have an average physical separation between the electron and hole, referred to as the exciton Bohr radius. This is a physical distance which is different for each material. The dimensions of semiconductor crystals are much larger in bulk semiconductors than the exciton Bohr radius, allowing the exciton to extend to its natural limit. When the size (diameter) of a semiconductor crystal becomes small enough that it approaches the size of the material's exciton Bohr radius, then the electron energy levels can no longer be treated as continuous. In this case, the electron energy levels must be treated as discrete. This means that there is a small and finite separation between energy levels. This situation of discrete energy levels is called quantum confinement. Under these conditions, the semiconductor material ceases to resemble bulk and instead is called a quantum dot. This has large repercussions on the absorptive and emissive behavior of the semiconductor material and thus on the applications quantum dots can be used for. With quantum dots, the size of the bandgap of the material may be controlled simply by adjusting the size of the dot. Because the emission frequency of a dot is dependent on the bandgap, it is therefore possible to control the output wavelength of a dot with extreme precision.
Although quantum dots have many promising applications, such as their use in lasers, single electron transistors or others, it is not always easy to control the size of quantum dots and/or their precise location on the substrate. Up till now, quantum dots are formed by using electron beam (e-beam) lithography techniques. These lithography techniques use a focused beam of electrons to expose a resist. In these techniques no mask is used as the pattern is “written” directly into the resist by very fast scanning of the electron beam. With this technique a pattern transfer resolution of below 100 nm may be obtained. However, the resolution is limited by the proximity effect, i.e. by scattering of electrons in the irradiated resist. This proximity effect may be responsible for the size of the exposed resist area being larger than the diameter of the incident electron beam which thus limits the resolution of e-beam lithography. This may be a disadvantage when using e-beam lithography for forming quantum dots as the size of the quantum dot determines its properties. Another disadvantage of using e-beam lithography for making quantum dots is that it is not suitable for being used for mass production of devices comprising quantum dots because of this proximity effect.